Question

What is the maximum number of electrons that can fill the second principal energy level?

Short answer

Therefore, the maximum number of electrons that can fill the second principal energy level is 8.

Step-by-step solution

Identify the energy level

From the question, we understand that we are dealing with the second principal energy level, hence \( n = 2 \)

Apply the 2n^2 rule

The 2n^2 rule helps us determine the maximum number of electrons that can occupy a certain energy level in an atom. In this case, we substitute \( n = 2 \) into the formula, yielding \( 2 * 2^2 \)

Calculation

After substitution, we perform the calculation: \( 2 * 2^2 = 2 * 4 = 8 \)

Key concepts

Electron Configuration

Understanding electron configuration is crucial for grasping how atoms form bonds and exhibit various properties. Electron configuration refers to the distribution of electrons in an atom's orbitals. Orbitals are specific regions around an atom’s nucleus where electrons are likely to be found.

Imagine an atom as a series of shells, each capable of holding a certain number of electrons. Within these shells, there are subshells, denoted by the letters s, p, d, and f, which further organize electrons. The 's' subshell can hold 2 electrons, 'p' can hold 6, 'd' 10, and 'f' 14. Electrons fill these subshells in a specific order, following the Aufbau principle, which states that electrons occupy the lowest energy level available.

The second principal energy level, for instance, has one 's' subshell and three 'p' orbitals, leading to a maximum of 8 electrons occupying it. The electron configuration for the second level would then start with 2s and continue to 2p until all orbitals are filled.

Quantum Numbers

Quantum numbers are like addresses for electrons, giving us precise information about their location and behavior within the atom. There are four quantum numbers required to describe the characteristics of electrons completely:

• The principal quantum number (\( n \)): This indicates the energy level and relative size of the orbital where an electron is found. It can be any positive integer starting from 1.
• The azimuthal quantum number (\( l \)): It tells us about the shape of the orbital, ranging from 0 to \( n-1 \) for each energy level.
• The magnetic quantum number (\( m_l \) ): This number shows the orientation of the orbital in space and ranges from \( -l \) to \( +l \) including zero.
• The spin quantum number (\( m_s \) ): It indicates the two possible spin states of an electron, which can be either +1/2 or -1/2.

Together, these numbers not only predict the electron’s location but also ensure that each electron in an atom has a unique set of quantum numbers, a requirement known as the Pauli exclusion principle.

2n^2 Rule

The 2n^2 rule offers a simple way to determine the maximum number of electrons within a principal energy level of an atom. The 'n' in the rule stands for the principal quantum number, signifying the energy level being considered. You can apply the rule by simply squaring the quantum number and then doubling the result.

For instance, in our original exercise, to find the maximum number of electrons in the second principal energy level (\( n = 2 \)), the calculation would follow these steps:

1. Square the energy level: \( 2^2 = 4 \)
2. Double the resulting number: \( 2 * 4 = 8 \)

Therefore, using the 2n^2 rule, we conclude that a total of 8 electrons can fill the second energy level. This rule is fundamental in predicting electronic structure and consequently the chemical behavior of atoms.